This page
gives access to a set of conversion tables for determining the Julian
equivalent of Egyptian civil and lunar dates in the Ptolemaic era.
Two tables are provided: a table converting civil dates to Julian
dates, and a table notionally converting lunar dates to civil dates
according to the lunar cycle of pCarlsberg 9.

On 7
Appellaios (Mac.) = 17 Tybi (Eg.) year 9 of Ptolemy III = 7 March
238, a conclave of the Egyptian priesthood held in Canopus at the
command of the king issued the Canopic
Decree (OGIS
56) which, among other things, changed the civil calendar from
the wandering year of 365 days to a fixed year by the intercalation
of a leap day at the end of the year in every fourth year, so that
the heliacal rising of Sothis (Sirius) would occur on a fixed date, 1 Payni:

And
whereas feasts of the Benefactor Gods are celebrated each month in
the temples in accordance with the previously written decree, the
first (day) and the ninth and the twenty-fifth, and feasts and public
festivals are celebrated each year in honor of the other greatest
gods, (be it resolved)

for
there to be held each year a public festival in the temples and
throughout the whole country in honor of King Ptolemy and Queen
Berenike, the Benefactor Gods, on the day on which the star of Isis
rises, which is reckoned in the sacred writings to be the new year,
and which now in the ninth year is observed on the first day of the
month Pauni, at which time both the little Boubastia and the great
Boubastia are celebrated and the gathering of the crops and the rise
of the river takes place;

but
if, further, it happens that the rising of the star changes to
another day in four years, for the festival not to be moved but to be
held on the first of Pauni all the same, on which (day) it was
originally held in the ninth year,

and
to celebrate it for five days with the wearing of garlands and with
sacrifices and libations and what else that is fitting;

and,
in order also that the seasons may always do as they should, in
accordance with the now existing order of the universe, and that it
may not happen that some of the public feasts held in the winter are
ever held in the summer, the star changing by one day every four
years, and that others of those now held in the summer are held in
the winter in future times as has happened in the past and as would
be happening now, if the arrangement of the year remained of 360 days
plus the five days later brought into usage (be it resolved)

for
a one-day feast of the Benefactor Gods to be added every four years
to the five additional days before the new year,
in order that all may know that the former defect in the arrangement
of the seasons and the year and in the beliefs about the whole
ordering of the heavens has come to be corrected and made good by the
Benefactor Gods.

(trans. as
given by R. A. Bagnall)

This reform is
essentially identical to the
Alexandrian reform undertaken under Augustus, except that it
fixed the Julian equivalents of the reformed Egyptian year to those
of the wandering year of the early 230s BC rather than those of that
of the mid-20s BC. Thus, under the Canopic calendar, 1 Thoth = 21-23
October, while under the Alexandrian calendar 1 Thoth = 29/30 August.

The decree
does not explicitly state which year of the four year cycle starting
in year 9 of Ptolemy III would end in a 6th epagomenal day. However,
we are told that the reform was intended to fix the date of the
heliacal rising of Sothis at 1 Payni, and that a festival to be
celebrated in honour of Ptolemy III and Berenice II and lasting for 5
days was to start on that day, with an additional festival on the 6th
epagomenal day. We may therefore proceed by investigating what is
known about these events.

Since the date
of the Sothic rising was said to advance by 1 day every four years
against the 365-day Egyptian calendar, we may speak of a "Sothic
quadrennium" of 365+365+365+366 days. This is the same
quadrennium that underlies the Julian leap year cycle, but the two
are not necessarily in phase. Noting that 237 was a Julian leap year
(as highlighted in green), there
are four possible relationships between Canopic quadrennia and Julian
quadrennia, as shown in the following table. The 6-day Epagomenes,
and the Julian dates of 1 Payni, are highlighted. For reasons
discussed below, the most likely cycle is that in which 6 Epagomene
fell at the end of cycle year 1 or 2.

Thoth

Phaophi

Hathyr

Choiak

Tybi

Mecheir

Phamenoth

Pharmouthi

Pachon

Payni

Epeiph

Mesore

Epagomene

6
Epagomene in Canopic year 1 = 239/8

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

23-Oct

22-Nov

22-Dec

21-Jan

20-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

6
Epagomene in Canopic year 2 = 238/7

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

20-Mar

19-Apr

19-May

18-Jun

18-Jul

17-Aug

16-Sep

16-Oct

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

6
Epagomene in Canopic year 3 = 237/6

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

20-Mar

19-Apr

19-May

18-Jun

18-Jul

17-Aug

16-Sep

16-Oct

21-Oct

20-Nov

20-Dec

19-Jan

18-Feb

20-Mar

19-Apr

19-May

18-Jun

18-Jul

17-Aug

16-Sep

16-Oct

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

6
Epagomene in Canopic year 4 = 236/5

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

21-Mar

20-Apr

20-May

19-Jun

19-Jul

18-Aug

17-Sep

17-Oct

22-Oct

21-Nov

21-Dec

20-Jan

19-Feb

20-Mar

19-Apr

19-May

18-Jun

18-Jul

17-Aug

16-Sep

16-Oct

21-Oct

20-Nov

20-Dec

19-Jan

18-Feb

20-Mar

19-Apr

19-May

18-Jun

18-Jul

17-Aug

16-Sep

16-Oct

21-Oct

20-Nov

20-Dec

19-Jan

18-Feb

20-Mar

19-Apr

19-May

18-Jun

18-Jul

17-Aug

16-Sep

16-Oct

A second
rising of Sothis is reported on 1 Thoth = 20 July AD 139 inCensorinus
21.10, writing in AD 238. He notes that it marked the start of
the Egyptian "Great Year", and occurred exactly 100 years
before the birthdate of his patron (counting inclusively) on 20 July
AD 238. This gives us the phase of the Sothic quadrennium: AD 139 is
the first year Sirius rose on 1 Thoth. Hence the Sothic quadrennium
was fixed at 19, 19, 19, 20 July in the second century AD (expressed
in phase sync with the Julian cycle, i.e. from AD 136-139, as is conventional).

The
reliability of Censorinus' account has recently been challenged by P.
F. O'Mara, JNES 62
(2003) 17, who argued that Censorinus' prime purpose was to
exalt the birthday of his patron, and therefore that his data need
not be historically accurate. He noted that Censorinus does not
elsewhere show any familiarity with Egyptian practice, and that
various ancient authorities give a number of dates for the heliacal
rising, ranging from 19 July to 22 July. He supposed that Censorinus
selected the date most appropriate to his purpose, as occurring
exactly a century before the birthday of his patron. In particular he
notes that Censorinus' date is unsourced, and that he states that
Sothis "customarily" rises on 21 July (a.d. XII Kal. Aug.)
in Egypt, which is conventionally amended to 20 July (a.d. XIII Kal.
Aug.), but the centennial anniversary he describes actually requires
that Sothis rose on 19 July for 3 years out of 4. He concludes that
Censorinus' account could well be explained by his having simply
subtracted 25 days from 20 July to find the Julian equivalent of 1
Thoth in AD 139, and then selecting the date given by an authority
for the Sothic rising that fits that result. Therefore, he concludes,
the date of the Sothic rising given in Censorinus cannot be assumed
to be correct. By way of illustration, he suggests that Censorinus
would have reached exactly the same conclusion if he had been writing
in AD 235, 236 or 237 -- i.e. he would have using exactly the same
reasoning to date the start of the Great Year to AD 136, 137 or 138.

O'Mara
makes some interesting and worthwhile points about Censorinus'
motives, his lack of expertise in Egyptian matters, and his
understanding and manipulation of the facts he presents. However, he
does not show (or argue) that Censorinus changed any of his
source material, only that he selected material that met his
need; nor does he show that Censorinus selected any facts which are
actually incorrect. The most he shows is that Censorinus makes some
questionable use of his facts on his client's behalf. Hence
the more relevant question is how reliable were Censorinus' sources.

Censorinus'
known sources (Varro, Suetonius etc.) being reputable (or considered
so in his time), one might argue against O'Mara that, since
Censorinus is not deeply familiar with Egyptian material, but does
generally present accurate material, the fact that he chose this
particular datum shows that it was actually well known in his time.
In any case, given the minor role Egyptian material plays in his
work, it is hard to imagine that he plucked the coincidence out of
the air, as O'Mara implies: he got it from somewhere. The fact that
he slightly misrepresents the significance of the datum, by
explaining that 2[0] July was the "customary" date, rather
than the date on which the rising was observed, strongly suggests to
me that in fact the datum itself is accurate.

As
to relevant errors in Censorinus' account, O'Mara cites two:

As
noted, Censorinus gives 21 July as the "customary" date
for the rising, not 20 July. However, O'Mara himself accepts the
usual MS emendation from 21 to 20 July, since 21 July is not
consistent with the equation 1 Thoth = a.d. VII Kal. Iul. (25 June)
which Censorinus gives, correctly, for 1 Thoth in AD 238 (and it is
easy to see how "a.d. XIII Kal. Aug." could be corrupted to
"a.d. XII Kal. Aug.").

The
standard emendation goes back to Scaliger (J. J. Scaliger, De EmendationeTemporum, 138).
In view of the debate over whether the Egyptian day began at
dawn or sunrise, it is perhaps worth noting that 21 July could in
fact be the correct date for the heliacal rising, if 1 Thoth began at
sunrise on 20 July AD 139. However, Censorinus' wording does suggest
that the equation 1 Thoth = 2[0] July in AD 139 was retrocalculated
from the equation 1 Thoth = 25 June in AD 238 (if not necessarily by
him), and 21 July is not the correct result for that. Moreover, 20
July is consistent with modern astronomical retrocalculations (see below).

Censorinus
equates AD 238 with year 267 of the era of the Roman rule in Egypt
(starting in 30 BC), when, in O'Mara's view, it should have been year
268. But the number 267 is in fact correct, as has long been known
(cf. A. T. Grafton & N. M. Swerdlow, CQ 35 (1985) 454
at 454). The point is to understand how it was calculated. While
Censorinus states that he calculates his Roman years based on a new
year of 1 January, he also clearly states that Egyptian years start
on 1 Thoth. He sets the epoch for the Egyptian era by stating that
Roman rule in Egypt started two years before Augustus took the
imperium, in February 27 BC. In Julian terms, Roman rule in Egypt
started three years before Augustus took the imperium, but in
Egyptian terms Augustus' assumption of imperium fell in his Egyptian
year 3. Therefore, in this instance Censorinus is calculating the
year of the Egyptian era according to the Egyptian (Alexandrian)
calendar, and 20 July AD 238 falls in Egyptian year 267 of an era
starting on 1 Thoth in 30 BC, not year 268. It is O'Mara, not
Censorinus, who is wrong.

O'Mara's
hypothetical scenario, intended to show how Censorinus might have
set the start of the Great Year to any year in the interval AD
136-139 if he had been writing in any year in the range AD 235-238,
is difficult to sustain. The purpose of Censorinus' tract was to
glorify his patron, here by noting that his birthday marked the start
of year 100 of the Egyptian Great Year. While Censorinus is the
earliest surviving author to explicitly attest to a Sothic Great
Year, he surely did not invent it. His primary source appears to have
been Varro's lost Antiquitates Rerum Humanarum. Varro
certainly made use of Egyptian data and may well have been mentioned
the Sothic Great Year. The concept of the "Great Year" was
well-known in his time, and it is evident from the Canopic Decree
that the specific concept of the 1460/1461-year Sothic cycle, which
defines the period of the Great Year, was well understood by
Alexandrian astronomers. Therefore there is every reason to believe
that the concept of the Sothic Great Year is much older than A.D.
139. The actual date of the start of the Sothic Great Year would
certainly have been observed and would have been known to Censorinus'
astrologically literate contemporaries. If he had got it wrong, he
would have opened up his patron not to praise but to ridicule.

Once
we accept that the Great Year was not Censorinus' invention, it is
easy to see how he could have reached his result without doing any
calculations at all. He leads up to the Sothic equation by giving the
(correct) current year number in multiple different epochs: Ol. 254.2
= A.U.C. 991 = Caesar 283 = Augustus (Julian) 265 = Augustus
(Alexandrian) 267 = Nabonassar 986 = Philip 562; this 7-calendar
synchronism was, for Scaliger and other early modern chronologists,
one of the most important data items they used to establish ancient
chronology. Censorinus also goes into great detail about the start
date of each year, in preparation for explaining the anniversary of
the Great Year. The last two of the dates, those of the eras of Nabonassar
and Philip, are based on the
same wandering Egyptian calendar as the Great Year. All three of
these eras are astronomical; indeed, Censorinus is the only surviving
ancient source for the first two outside the Almagest. Almost
certainly, he got all of these dates from a single source, and since
this source included two other astronomical dates it is surely also
the source of the third.

Finally,
not discussed by O'Mara, but long ago noted by L. Borchardt, Die Annalen
und die zeitlichen
Festlegung des alten Reiches
der ägyptischen Geschichte 55, Alexandrian coins of years 2
and 6 of Antoninus Pius = AD 139 and AD 143 are known showing a
phoenix and bearing the legend AIWN.
While these coins do not specifically mention Sothis, they fit
perfectly with the notion that they mark the beginning and the end of
the quadrennium in which the heliacal rising of Sothis fell on 1
Thoth, marking the start of the Sothic cycle, and no other
explanation is known. If this event received so much public attention
that it was commemorated in coinage, it is quite reasonable to
suppose that it was still well-known a century later.

In
short, O'Mara has not proved his case, and the conventional analysis
of Censorinus is much more likely than not. The remainder of the
discussion here assumes that the standard interpretation of
Censorinus is in fact correct and that it accurately reflects what happened.

Given the
phase of the Sothic rising against the Julian quadrennium in AD 139,
and assuming, with the ancients, that the period of the Sothic cycle
against the Egyptian wandering years was exactly fixed at 1460
(Julian) years, one would expect the phase of the Sothic rising at
the time of the Canopic Decree to be the same. However there is an
immediate problem: 238 BC, like AD 139, is the last year of a Julian
quadrennium, but in this year 1 Payni fell on 19 July, not 20 July.

One possible
explanation of the discrepancy between Canopus and Censorinus was
advocated by L. Borchardt (as reported by R. Krauss, Sothis- und Monddaten,
59): that the Canopic decree was based on observations made to the
south of Alexandria/Canopus. In general, the heliacal rising in Egypt
occurs about 1 day earlier for each additional degree of latitude
south of the Mediterranean coast. Borchardt's preferred sites,
Memphis or Heliopolis, are about a degree south of Alexandria, hence
a heliacal rising of 20 July in Alexandria generally corresponds to a
rising of 19 July at these sites. However, R. Krauss, Sothis- und Monddaten 58,
has calculated the likely Julian quadrennia for the heliacal
rising of Sothis at the latitude of Memphis assuming an arcus visionis
of between 8° and 9°. His model showed a cycle of 18, 18,
18, 19 July at the time of Censorinus, as expected, which lends
confidence in his result for the time of the Canopic Decree: 17, 18,
18, 18 July. Hence it is very unlikely that the Canopic observations
were made at Memphis. Indeed, the predicted cycle for
Alexandria/Canopus in 238 on Krauss' model is 18, 19, 19, 19 July,
which is entirely consistent with the Canopic decree. Nevertheless,
the possibility that the Canopic date is not based on an observation
at the latitude of Alexandria/Canopus cannot be completely excluded;
it just does not seem to be necessary to consider it.

The most
likely source of the discrepancy, and one which appears to be
sufficient to explain it, is slippage of the astronomical Sothic
quadrennium against the Julian one between 238 and A.D. 139. The
astronomical Sothic cycle is slightly different from the cycle of
1460 Julian years assumed by classical authors and changes over time
due to factors such as the precession of the earth about its axis. M.
F. Ingham, JEA 55 (1969) 36, calculated that the cycle
ending c. AD 138 was about 1452 or 1453 years long. This means that
the date of the heliacal rising slipped 7 or 8 days against the
Julian calendar over the course of that cycle. If one assumed a
constant rate of change, this would be roughly 1 day every 181 or 207
years. Since the period of the astronomical Sothic cycle is itself
getting slightly shorter over time, the chances are that the actual
intervals between slips of a day between 238 and AD 139 are slightly
shorter than these averages.

The actual
dates of the slippages will depend on second-order factors which are
difficult to determine precisely. However, we can say that the most
likely aggregate slippages over the 376 years from 238 to AD 139 are
1, 2 or 3 days, depending on the phase of the slip against this
interval, with by far the most probable slip being 2, then 3, then 1,
and a slip of 4 or more days being very improbable. Any discrepancy
greater than 3 days probably requires additional factors, most likely
including a change in the place of observation, but for 3 days or
less no additional factors are required.

Ingham's model
is not unchallenged. B. E. Schaefer, JHA 31
(2000) 149, based on his own model of atmospheric effects and
assuming arcus visionis of around 11°, estimates a net
slip of only 0.1 days against the Julian calendar at Memphis between
c. 500 BC and A.D. 1 and 2 days between A.D. 1 and A.D. 500, i.e.
about 0.6 days between c. 238 B.C. and A.D. 139. Since this is an
average figure, and since a slip certainly occurred, the effective
slip on Schaefer's model will be 1 day.

Working
backwards from AD 139, the candidate Canopic quadrennia in 238 at the
latitude of Alexandria and Canopus are therefore:

19, 19, 19, 20
July in AD 136-13919, 19, 19, 19
July for a slip of 1 day between 241-238 BC and AD 136-13918, 19, 19, 19
July for a slip of 2 days between 241-238 BC and AD 136-13918, 18, 19, 19
July for a slip of 3 days between 241-238 BC and AD 136-139

The cycle for
a 2 day slip matches the cycle predicted by Krauss' model for Memphis
in 238, discussed above.

The question
of how these slips would have been reflected in the Canopic calendar
has been much discussed: was the Canopic leap-year cycle
observationally based or schematic? R. Krauss, Sothis- und Monddaten
54ff, concludes that the calendar was schematic. He presents two
arguments for this. The first, based on his analysis of the language
of the decree, concludes that the Canopic leap year cycle was the
same as that of Censorinus, i.e. 19, 19, 19, 20 July, a cycle which
could not have been observationally based at that time. This (in my
opinion highly improbable) argument is considered further below.
The second, more briefly stated, is that the Canopic decree is the
product of Graeco-Roman astronomy, and that all other statements made
in classical authors about the Sothic cycle clearly refer to a fixed
schematic cycle of 1460 solar years, showing no evidence of
understanding that an occasional phase slip would occur. In my view,
this argument is rather more persuasive.

In any case,
these phase slips are very rare. Nevertheless, the case of a net slip
of 3 days between the Canopic and Censorinus sightings is potentially
important because the first such slip would most likely have occurred
within a very few years of the promulgation of the reform. L. E.
Rose, Sun, Moon and Sothis, 188f, suggests that this is
exactly what happened, and that the Canopic reform failed for
precisely this reason. However, while we cannot exclude a net slip of
3 days, it seems to me rather unlikely that the reform failed for
this reason.

First,
granting the scenario for the sake of argument, the first few
instances of the slip might easily be put down to observational
errors, especially since they would only occur one year in four even
if viewing conditions were perfect.

Second,
the decree itself contained a provision that recognised that the
Sothic rising might not occur on the expected day. The implications
of this provision are considered further below.

Third,
the evidence of the Macedonian double dates considered below
suggests that in fact the reform was not abandoned for a considerable time.

Returning to
the phase of the Canopic intercalary cycle with this background, I
have found three positions in the recent literature.

R. A. Parker,
in Fs Hughes, 177 at 186, following a comment by G. H.
Wheeler, JEA 9 (1923) 6, argued that the language of the
Canopic Decree ("on
the day on which the star of Isis rises ... which now in the ninth
year is observed on the first day of the month Pauni")
implies that a Sothic rising had already been observed on 1
Payni of the ninth year. Given the date of the Decree (7 Appellaios =
17 Tybi year 9) this would only be possible if the ninth year is the
Macedonian year, in which case the decree itself tells us that 1
Payni year 8 (Eg.) = 19 July 239 was also a Sothic rising. Hence,
Parker's analysis implies that the Decree gives us that the Canopic
Sothic quadrennium was X, X, 19, 19 July, which concurs with the
above analysis of the possible
quadrennia derivable from Censorinus, but does not refine it. The
argument, if correct, does show that a gain of 4
days between 238 BC and AD 139, giving a Canopic quadrennium of 18,
18, 18, 19 July, is not possible, but in any case this is a very
improbable number.

A. J.
Spalinger, in idem., Three
Studies on Egyptian Feasts and Their Chronological Implications,
31 at 40, argues that syntactical anaysis of the language of the
Decree actually implies that it was simply stating an accepted fact,
similar to the statement that the birthday of the king was on 5 Dios,
and that the general usage of calendars in the operational statements
of the decree requires the Egyptian calendar to be in use. He notes
in particular that the priests to be enrolled in the fifth phyle
included "those
who are to be assigned until the month Mesore of the ninth year";
the use of the future tense can only apply if the year is the ninth
Egyptian year. It would follow that we cannot conclude that the
decree is stating that a rising was observed on 19 July 239, although
we also cannot exclude it. (L. E. Rose, Sun, Moon and Sothis,
154, also disagrees with Parker's interpretation, though he
misidentifies the text on which it was based.)

Spalinger
does not conclude that Parker was wrong about the Canopic cycle,
only that the Decree itself only allows us to infer X, X, X, 19 July.
However, 1 Payni equates to 19 July in both year 8 and year 9 of
Ptolemy III (Eg.) = 239 and 238. If Sothis did not rise on 19 July
239, the only possible alternative for year 8 (Eg.) is 18 July 239
(=30 Pachon year 8). In this case, Spalinger's argument would require
a gain of 4 days between 238 and AD 139. While this is not absolutely
impossible, especially if the Canopic observation was not made in
Alexandria, this assumption does not otherwise seem to be necessary.
Therefore, even if the language of the decree does not offer
irrefutable proof that risings occurred on 19 July 239 (and 238),
rather than 18 July, this remains the most likely sequence of events.

L. E. Rose, Sun,
Moon and Sothis, 178ff, argues (p181) that the slip between 238
and AD 139 must be precisely three days, on the grounds that a slip
of two days (or one) would imply a Sothic rising on 1 Payni = 19 July
in 240. He supposes that the Decree shows that the rising on 1 Payni
in 239 was the first such rising on that date, which would
imply that the previous rising was on 30 Pachon year 7 (Eg.) = 18
July 240.

However,
the Decree says no such thing, and Rose presents no argument that
this interpretation is required.

R.
Krauss, Sothis- und Monddaten 54ff, notes that, shortly
before introducing the reform, the decree states "but
if, further, it happens that the rising of the star changes to
another day in four years, for the festivalnot
to be moved but to be held on the first of Pauni all the same".
He connects this to the fact that there was no possibility of a 6
Epagomene between the date of the promulgation of the reform (17
Tybi) and the next 1 Payni thereafter, and infers that the reason for
the provision is that it was expected that the heliacal rising would
in fact not occur on 1 Payni in 238, but on 2 Payni, and would
occur on 1 Payni thereafter because a 6 Epagomene was inserted at the
end of that year. If so, the Julian cycle implied by the decree is
19, 19, 19, 20 July -- the same as the cycle of Censorinus! Since,
however, this cannot be the astronomical cycle in Alexandria/Canopus
or anywhere in Egypt at this time, he concludes that the Canopic
cycle is completely schematic, and is not tied to any observed rising
of Sothis. He argues that this cycle was a fixed offset from a
schematic cycle of either 17, 17, 17, 18 July or 18, 18, 18, 19 July,
which was set in Memphis in the early 1st millenium.

There
is perhaps some uncertainty as to the translation. Krauss' argument
requires that the passage means that a change could occur within the
four years of the intercalary cycle. However, A. J. Spalinger, in
idem., Three
Studies on Egyptian Feasts and Their Chronological Implications,
31 at 36 translates the same passage as "But
if it occurs that the heliacal rising of the star changes to another
day at the interval of four years"
and comments "This is an obvious
condition of fact". If so, the whole
basis of Krauss' argument would disappear; instead, the passage would
simply be motivating the substance of the reform. I cannot comment on
the Egyptian or the Greek, but I have to wonder why, if the clause
is, as Spalinger says, a statement of fact, it would be constructed
as a conditional premise. Further, the actual motivation for the 6th
epagomenal day is very clearly spelled out in the following section,
that it is intended to ensure that the feasts which are fixed in the
Egyptian year remain fixed against the seasons. It seems to me much
more reasonable to interpret the clause in question as fixing the
calendar date of the Sothic festival even if the heliacal rising is
not observed on that date, just as Krauss suggests.

Assuming
that the interpetation used by Krauss is correct, therefore, it
follows that the Decree allows for the rising not to occur on 1 Payni
within a four year cycle, and I agree with him that this is clear
evidence that the cycle was intended to be schematic in its phase
alignment to Sothis. However, I cannot agree that we must therefore
infer that the rising in fact occurred on 2 Payni in 238 --
especially since by Krauss' own admission such a rising was not real!
If in fact the cycle is schematic to such an extent that it is even
based on virtual heliacal risings, as Krauss supposes, it seems to me
we are back to square one: why was it necessary to provide for the possibility
of a feast occurring in a year in which a virtual rising occurs on a
different date? It would be known with certainty, by design, whether
or not the virtual rising would occur.

The
notion that the Canopic cycle was based on a Memphite cycle set
early in the first millenium BC also strikes me as highly improbable.
As Krauss himself points out, the Sothic cycle of 1460 years is only
known as a schema of Graeco-Roman astronomy. There would be no reason
to fix a quadrennium except within the context of such a schematic
astronomy, and there is no evidence whatsoever that the Egyptians
were practicing such an astronomy early in the first millenium BC.
Rather, we should expect the Canopic cycle to be a schematic cycle
grounded in the observational reality of the time the decree was
passed, i.e. the third century BC, and almost certainly invented by
the Greeks. But, even this possibility does not match Krauss' model:
his schematic cycle would not converge with reality for nearly 4 centuries.

Moreove,
there is another way to interpret this provision of the decree,
which Krauss does not consider, but which is in line with his premise
and is not nearly so speculative: not that the rising could be late
in 238, but that it might be early. If the actual rising in
239 was on 30 Pachon = 18 July, the statement that "in
the ninth year [it] is observed on the first day of the month Pauni"
would be predicting a 366-day interval. If the interval turned out
to be 365 days, the rising might then be observed again on 30 Pachon
= 18 July in 238. So, one could interpret the provision as an
indication that the Julian quadrennium was actually 18, 18, 18, 19
July, possibly just after the slip from 18, 18, 18, 18 July to 18,
18, 18, 19 July. However this interpretation is open to the same
objection noted above that it implies 4 days slip between 238 and 139 BC.

While
my German is poor enough that I may have misconstrued some aspect of
Krauss' argument, it seems to me to be more grounded in his belief
that Sothic dates were set at a national observatory (now Memphis,
previously Elephantine) than in the actual evidence of the Canopic
Decree. Although it is not clear why it was felt necessary to provide
for the possibility of a Sothic rising that did not fall on 1 Payni,
there is no obvious reason why it should necessarily be tied
specifically to the Sothic rising of 238, rather than being (as it
appears to be) general insurance for a possible event.

The
Canopic calendar is grounded in the quadrennial model, which implies
that the quadrennial phase shift was clear enough in the
observational records on which the decree was based for there to have
been confidence in its predictability. Nevertheless, there are many
sources of variation that could affect the date of any particular
observation in any particular place, of which poor observation is
only the most obvious. B. E. Schaefer, JHA 31
(2000) 149 at 151 estimates that variations in the estimated
extinction coefficient of one standard deviation alone is enough to
cause variations of two days in the observed heliacal rise day.
Whether his particular model is right or not, his underlying point,
that an isolated observational datum may not be trustworthy, is
surely correct. The fact must also have been known to the astronomers
who devised the calendar, and this provision is most likely intended
to accommodate it.

Unless
Censorinus is not reliable, it seems to me that the three quadrennia
listed above are the only realistic possibilities, although a 4-day
discrepancy might just be possible if the Decree was based on
observations made to the south of Alexandria/Canopus. I conclude that
the Canopic leap year was almost certainly not at the end of cycle
year 4, and was most likely at the end of cycle year 1 or 2. However,
no possibility can be completely excluded at this time.

The
Longevity of the Canopic Reform

There is no
doubt that the Canopic reform failed. The
wandering year continued to be in general use, and the
Alexandrian reform proves that the Canopic reform had been
abandoned before the Roman conquest. This does not mean that it was
never implemented. Like the Alexandrian calendar, it may well have
coexisted alongside the wandering year for some time. However, since
Lepsius first published the Canopic Decree in 1866, the question of
how long it was followed by any segment of Ptolemaic society has
received very little attention, presumably for apparent lack of evidence.

C. R. Lepsius, Das
Dekret von Kanopus, 14, speculated that the feast of the
Benefactor Gods to be held on the 6th epagomenal day was probably
celebrated during the reign of Ptolemy III, in 238, 234, 230, 266 and
222 (i.e. in Canopic cycle year 1) and abandoned thereafter. This
view has recently been endorsed by S. Pfeiffer, Das Dekret von
Kanopus (238 v. Chr.) 257. The speculation is completely
reasonable and may well be correct, at least for the reign of Ptolemy
III, but, as a matter of logic, even if there were evidence for the
celebration of the feast it would not actually be relevant to the
calendrical issue unless that evidence were explicitly dated. Indeed,
as noted above, the Decree contains a provision that anticipates that
the heliacal Sothic rising might occur on a day other than 1 Payni,
and fixes the date of the festival at 1 Payni (Canopic), so the only
proof we could hope for is a date for the start of the festival that
was not 1 Payni.

Even a date
would need to be handled with care. On the one hand, it would have
been perfectly possible for the festival to be celebrated on the
wandering calendar even during Ptolemy III's reign, with the date
advancing by one day every four years. On the other hand, even if the
feast was abandoned by the priesthood after the death of king, that
need not necessarily imply abandonment of the 6th epagomenal day,
even by the priestood, let alone by the Ptolemaic bureaucracy.

The de facto
position of modern Egyptology on this question is summarised by A. E.
Samuel, Ptolemaic Chronology 76, who bluntly stated "There
is no evidence that this decree ever had any effect on the Egyptian calendar".
This view effectively denies that the reform was ever implemented at
all, a position which seems rather unlikely given the effort that
went into propagating the decree and the fact that other aspects --
notably the creation of a fifth priestly phyle -- certainly were implemented.

The only
attempt I have found to address this question directly is a limited
analysis by S. Pfeiffer, Das Dekret von Kanopus (238 v. Chr.)
250f. Pfeiffer sought to bound the life of the Canopic reform by
looking for occurrences of epagomenal dates in Canopic cycle year 1,
which he supposed to be the Canopic leap year, following Lepsius. He
found that pTebt 3.2.841
explicitly referred to the 5 epagomenal days in 114, which in his
view was a candidate Canopic leap year. He concuded that the reform
must have been abandoned by this time.

This approach
is inherently flawed, since (a) as noted above we don't know the
phase of the Canopic leap year (and Pfeiffer did not choose the most
probable phase) (b) the evidence of the Alexandrian calendar suggests
that the Canopic and wandering years most likely coexisted, and we
have no definitive criteria for deciding when to expect a given date
of Egyptian form to be given according to the Canopic year or the
wandering year. In any case, since only 1 day out of 1461 is a leap
day, the probability of any given surviving document being so dated
is vanishingly small. For comparison, the earliest known document
dated to 6 Epagomene (Alexandrian) is pOxy 1.45,
dated 6 Epagomene year 14 of Domitian = 29 August AD 95 -- 120 years
after the introduction of the reform. Similarly, the earliest known
document dated by the bissextile day of the Julian calendar is CIL
VIII 6979, which records a temple dedication on the day after the
bissextile (leap day) in AD 168 -- 212 years after the Julian reform.

Contemporary
evidence for the analogous Alexandrian reform suggests two other
methods for demonstrating use of the Canopic reform: Dates explicitly
distinguishing the Canopic and wandering calendars, or double dates
between Egyptian dates according to the Canopic calendar (whether so
stated or not) and a second calendar.

No
Ptolemaic-era dates have been found that are explicitly identified as
being according to either the Canopic or the wandering calendar (or
at least there are none recognised in any literature that I have
seen). Again, the Alexandrian calendar suggests this is not
surprising. The earliest such date recorded in D.
Hagedorn & K. A. Worp, ZPE 104
(1994) 243 is BGU 3.957, a horoscope (probably) dated under the
["old"] (i.e. wandering) calendar in 10 BC, and many of the
early examples of such formulae are from similar astrological texts,
which are not yet in evidence in the early Ptolemaic period.

Aside from
astrological texts, the earliest contemporary evidence for the
Alexandrian calendar consists of double dates with a second calendar.
The earliest explicit double date between the Alexandrian and
wandering calendars is SB 1.684, which is dated to 18 Tybi = 1
Mecheir "according to the Egyptians" in year 17 Tiberius =
13 January AD 31, 57 years after the Alexandrian reform. However,
much earlier double dates are known with other calendars: the
Egyptian lunar calendar in 10 BC (pdem Rhind 1), and the Roman
calendar in (most probably) 8-6 BC (pVindob
L.1c) and in either 24 BC or, perhaps more likely, AD 3 or AD 7 (SB 18.13849)
-- all within 30 years of the reform.

This suggests
that evidence for use of the Canopic calendar, if it exists, is most
likely to be found in Egyptian/Macedonian double dates after year 9
of Ptolemy III. The double dates of this period have long resisted a
clear resolution. The Zenon papyri clearly demonstrated that the
official Macedonian calendar under Ptolemy II was a lunar calendar,
although the lunar phase of the first day of the month was only
determined to within a day or two's precision. Also, provincial use,
exemplified by the dockets generated in Zenon's office, shows a
tendency towards simplification through a fixed alignment to the
Egyptian calendar. The known simplifications are to equate months
directly or to place them 10 days out of phase, though even the Zenon
papyri contain double dates from Zenon's office that are not lunar
but also do not conform to either of these algorithms. For this
reason, the best matches should be expected from documents that can
be tied to an Alexandrian source, while greater latitude may be
allowed from documents from other sources.

T. C. Skeat, JEA
34 (1948) 75, was able to propose an arrangement of the known double
dates of Ptolemy III which preserved an approximate lunar alignment,
but one that was apparently less precise than that prevailing under
Ptolemy II. However, in order to do so he needed to assume that some
of these documents were dated according to the financial
year. This assumption was strongly attacked by A. E. Samuel, Ptolemaic
Chronology 81, whose analysis has not been challenged since, so
far as I can determine, although his individual arguments can all be overturned.

Samuel was not
able to propose a better model than Skeat's, and indeed concluded
"we must admit that the regulation of the Macedonian calendar
during the reign of Euergetes was varied and uncertain at best".
This conclusion should in itself have been an indication that there
was a problem with Samuel's approach. In light of the apparent
weakness of his arguments, the only significant objection I see to
Skeat's empirical approach is that the lunar alignment appears to be
weak after Ptolemy II. But this is exactly what we would expect to
see if the Egyptian side of an Egyptian/Macedonian double date was a
Canopic date which was misinterpreted as a wandering date -- indeed
it should appear to become weaker over time.

So far as I
can determine, no one has attempted to analyse these double dates
while allowing for the possibility that some of the Egyptian dates
may be based on the Canopic calendar. The closest is a paper by M. L.
Strack, RhMP 53 (1898) 399, who attempted to analyse the
double dates known to him against the wandering year and a Sothic
year based on 1 Thoth = 19 July. This approach was immediately,
roundly, and rightly rejected by his contemporaries, since there is
no reason to suppose that the Sothic calendar exists, and his paper
has been completely ignored since. However, his basic insight that a
second Egyptian calendar may be involved in addition to the wandering
year deserves consideration, since we know that such a calendar did
in fact exist. Strack rejected the Canopic calendar as a basis for
analysis since the evidence shows that the wandering year was
unaffected by the reform. Although he supposed that the Sothic year
existed alongside the wandering year, he seems never to have
considered that the same might be true for the Canopic year.

The following
table contains an analysis against the wandering year and the Canopic
for the double dates known to me of Ptolemy III and later which
appear to show independent operation of the Macedonian calendar (as
always, if you know of others please email
me). It assumes that the Macedonian dates are lunar. Consequently,
the year number is interpreted according to the C[ivil], F[inancial]
or M[acedonian] scheme(s) that give the best lunar match. Where it is
not certain whether the ruler involved is Ptolemy III, IV, V or VI,
the date is likewise assigned to the king who gives the best lunar
match. Each double date is linked to a discussion page giving the
issues related to that item.

It will be
seen that most, though not all, of those double dates which do not
match the wandering year can be resolved by assuming that the
Egyptian date was according to the Canopic year. From this table, we
may conclude that the Ptolemaic administration probably used the
Canopic calendar intermittently until the end of the reign of Ptolemy
VI, indeed until the Macedonian calendar was fully assimilated with
the Egyptian calendar under Ptolemy VIII, though not consistently.
The most interesting feature of the table is that the Canopic
calendar and the wandering calendar appear both to have been used by
the Ptolemaic administration, even in Alexandria. The significance of
this is unclear.

NB:
This version
is preliminary.
Research into individual items is still ongoing at this time.